Unifying quantum computation with projective measurements only and one-way quantum computation

Abstract

Abstract. Quantum measurement is universal for quantum computation (Nielsen [4], Raussendorf [7,8]). Two models for performing measurement-based quantum computation exist: the one-way quantum computer was introduced by Briegel and Raussendorf [7], and quantum computation via projective measurements only by Nielsen [4]. The more recent development of this second model is based on state transfers [6] instead of teleportation. From this development, a finite but approximate quantum universal family of observables is exhibited, which includes only one two-qubit observable, while others are one-qubit observables [6]. In this article, an infinite but exact quantum universal family of observables is proposed, including also only one two-qubit observable. The rest of the paper is dedicated to compare these two models of measurement-based quantum computation, i.e. one-way quantum computation and quantum computation via projective measurements only. From this comparison, which was initiated by Cirac and Verstraete [9], closer and more natural connections appear between these two models. These close connections lead to a unified view of measurement-based quantum computation.

Discrete Wigner functions and quantum computational speedup

“…This idea was first suggested by Shor [31], and has since been elaborated on by other authors [32,33,34,35,36].…”

Universality of measurements on quantum markets

“…Much more additional qubits are necessary if the corresponding supply and demand curves are continuous (floating point precision) -one qubit for each binary digit of the logarithm of price). However, these are theoretically unimportant details -all such forms of quantum markets can be implemented with the use of elementary market measurements alone what follows from the analysis by Nielsen, Raussendorf and Briegel, and Perdrix and Jorrand [17]- [21]. The rest of the paper is devoted to this problem.…”

“…The method used by Perdrix and Jorrand [20,21] to analyse the problem of universality in quantum computation can be easily adopted to the situation we are considering. Following Ref.…”

Measurement-Based Quantum Computing With Valence-Bond-Solids

“…Apart from the original discussion on how MBQC simulates these gates [16], there are other alternative discussions [41,42,43,44,45,46,19]. Here we would like to take the one provided by Nielsen in [19], which is in turn based on the circuit given in Fig.…”